A result which was known well before, and used to formulate the old quantum condition.
2.
It was an argument for the old quantum condition mostly independent from the one developed by adiabatic invariance.
3.
In 1924, as a PhD candidate, Louis de Broglie proposed a new interpretation of the quantum condition.
4.
I applied this rule to Heisenberg's quantum condition and found that it agreed for the diagonal elements.
5.
The motivation for the old quantum condition was the correspondence principle, complemented by the physical observation that the quantities which are quantized must be adiabatic invariants.
6.
The integral is easiest for a " particle in a box " of length " L ", where the quantum condition is:
7.
The old quantum condition requires that " J " multiplied by the period of \ theta is an integer multiple of Planck's constant:
8.
The level sets of " H " are the orbits, and the quantum condition is that the area enclosed by an orbit in phase space is an integer.
9.
This relation is attributed to Max Born ( 1925 ), who called it a " quantum condition " serving as a postulate of the theory; it was noted by Heisenberg uncertainty principle.
10.
In order for the old quantum condition to make sense, the classical motion must be separable, meaning that there are separate coordinates q _ i in terms of which the motion is periodic.
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